{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QRS4Z3O35MJGRVBKXPPIRKVIIC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c53af5f28892d714135da2adaba1174b411abaf1ae0b6db515b7df68240d0f8c","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-20T11:20:14Z","title_canon_sha256":"a109f3c31b0787f7732af1d4ac41e9edad3fcd4dbaf4eea9039fed5209ee3c43"},"schema_version":"1.0","source":{"id":"2506.16917","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.16917","created_at":"2026-07-05T11:24:44Z"},{"alias_kind":"arxiv_version","alias_value":"2506.16917v1","created_at":"2026-07-05T11:24:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.16917","created_at":"2026-07-05T11:24:44Z"},{"alias_kind":"pith_short_12","alias_value":"QRS4Z3O35MJG","created_at":"2026-07-05T11:24:44Z"},{"alias_kind":"pith_short_16","alias_value":"QRS4Z3O35MJGRVBK","created_at":"2026-07-05T11:24:44Z"},{"alias_kind":"pith_short_8","alias_value":"QRS4Z3O3","created_at":"2026-07-05T11:24:44Z"}],"graph_snapshots":[{"event_id":"sha256:b23a9d14a8c27098aca97e89818af10d47930ed7c93fbcad630bc85f03ec0ece","target":"graph","created_at":"2026-07-05T11:24:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.16917/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Error bounds for fully discrete schemes for the evolutionary incompressible Navier--Stokes equations are derived in this paper. For the time integration we apply BDF-$q$ methods, $q\\le 5$, for which error bounds for $q\\ge 3$ cannot be found in the literature. Inf-sup stable mixed finite elements are used as spatial approximation. First, we analyze the standard Galerkin method and second a grad-div stabilized method. The grad-div stabilization allows to prove error bounds with constants independent of inverse powers of the viscosity coefficient. We prove optimal bounds for the velocity and pres","authors_text":"Bosco Garc\\'ia-Archilla, Julia Novo, V. John","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-20T11:20:14Z","title":"Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16917","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9bdd61eecb90af9d589f19f018900fd984596d1e2a45b0dfea92ac90ef7aa5d7","target":"record","created_at":"2026-07-05T11:24:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c53af5f28892d714135da2adaba1174b411abaf1ae0b6db515b7df68240d0f8c","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-20T11:20:14Z","title_canon_sha256":"a109f3c31b0787f7732af1d4ac41e9edad3fcd4dbaf4eea9039fed5209ee3c43"},"schema_version":"1.0","source":{"id":"2506.16917","kind":"arxiv","version":1}},"canonical_sha256":"8465cceddbeb1268d42abbde88aaa840946c2f52e06f21dfff2e35aa47821390","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8465cceddbeb1268d42abbde88aaa840946c2f52e06f21dfff2e35aa47821390","first_computed_at":"2026-07-05T11:24:44.954541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:24:44.954541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tFBO0ETEqdJGn2yCn7IdXme2+0Z3UlZftaWFWTu+44LduORdh9mmqs+UEE2JCYIznXJ3WO6gr7sfBx9+3fTlBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:24:44.955092Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.16917","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bdd61eecb90af9d589f19f018900fd984596d1e2a45b0dfea92ac90ef7aa5d7","sha256:b23a9d14a8c27098aca97e89818af10d47930ed7c93fbcad630bc85f03ec0ece"],"state_sha256":"a23dca61fdb81af0ba2f193db30eddad3767c0b27040eb2185fe33163327a5e6"}